Those connections aren't going to have too much of a measurable effect on your flowrate in this system. The main factors are:
-Where is the pump getting it's feed water (i.e. what elevation)
-Where is the pump discharging the water
-What does the pump curve look like
Probably the pump is rated for a specific flow rate due to the relatively constant geometry of pool pumping systems. Ask the vendor/pool store.
The pump controls the flow, if it puts out 100 gallons per minute for your system conditions, then each wye section will see approximately 50 gallons per minute in both the 2 inch sections and the 1 inch sections. The reducer is there to increase the velocity of the water so that the pool gets a bit of circulation going, so the water doesn't remain stagnant. It does this to help the suspended particulates reach the filter rather than settling to the bottom.
Your flow rate will split more or less evenly among the two sections after the wye, it won't be exact (that's life) due to the fact that your system isn't exactly a precision-built one, but it'll be pretty close.
It is important here to note that the reducer doesn't act to reduce the flowrate (**read below), it transitions the pipe to a smaller diameter pipe where the flow velocity is increased, the effect of the water having to change direction is measurable, but in this case probably insignificant.
**You are probably aware that pumps work on a curve. If you know your system conditions, you can calculate where on that curve your pump is sitting (a bit iterative, since flowrate is found on the curve based on system head, system head is partially determined by pipe friction losses, and pipe friction losses are determined by flow rate!). The losses from all of your elevation changes, fittings, elbows, and friction due to flow rate will allow you to calculate the total head of the system, and thus get a good idea of where on its curve your pump should be operating.
To answer your question about the elbows/valves/reducers effect on flow rate:
When we discuss things like this, we don't discuss how they affect flow rate, we care about how they affect losses.
Elbows will have the least effect of the three (arguably, if the valves are ball valves, the elbows and valves will result in similar losses) with the valve coming in a close second.
As I mentioned before, the reducer will have only a slight effect on the system head (similar to an elbow), however because the downstream pipe is now smaller diameter, the flow velocity within it will be increased (since the whole system maintains an equal flow rate). This increased velocity results in additional friction due to the interaction with the viscous water and the pipe walls (and its imperfections), resulting in added system head that the pump must overcome, driving the pump back on its curve and resulting in a flowrate that is lower than if those 1" sections were 2" sections, but discharging at a higher velocity.
In short: You need the pump curve to determine the flowrate without actually physically measuring it.
